The fighting, which killed at least 15 people, threw war-torn Yemen into further chaos and threatened to undermine President Abedrabbo Mansour Hadi, who ordered his forces to stand down.
Security sources and residents said clashes appeared to have spread to most of the city.
The government urged the Saudi-led military coalition, which has been supporting Hadi against Iran-backed Huthi rebels who control much of the north, to intervene.
The southern separatists — who want the return of an independent state that ended with Yemen’s unification in 1990 — backed Hadi’s government against the Huthis but tensions between them had been rising.
“A coup is ongoing here in Aden against legitimacy and the country’s unity,” Prime Minister Ahmed bin Dagher said in a statement.
Shortly afterwards, it was reported loyalist commanders had received orders from Hadi to disengage.
“After talks with the Arab coalition… you must order all military units to cease fire immediately,” a government statement said.
On Sunday afternoon, coalition planes flew over the city.
Security sources told AFP that pro-separatist units trained and backed by the United Arab Emirates had taken over the government headquarters in Aden after clashes.
The 15 dead included three civilians, hospital sources said. Dozens were wounded.
Doctors Without Borders (MSF) tweeted that one of its facilities in Aden had received 50 wounded and four dead.
The fighting erupted after separatist protesters were prevented from entering the city for a rally to demand the government’s ouster from Aden, which became its de facto capital after the Huthis seized Sanaa in 2014.
The separatists accused the prime minister of ordering his troops to open fire at the protesters.
Separatist fighters and supporters danced at an intersection as truckloads of armed men drove through the streets.
By early evening, separatists took control of two roads leading to the presidential palace where several members of the government were staying, security sources said, adding that fighting had receded.
Schools, airport closed
Saudi and Emirati troops present in Aden did not intervene when the clashes first broke out, security sources said.
The coalition, which launched its intervention against the rebels in March 2015, had urged restraint ahead of the planned protest.
It called on all sides to “adhere to the language of calm dialogue”, the Saudi state news agency SPA said late Saturday.
The UAE also called for restraint and reiterated its support for the coalition’s mission in Yemen and its rejection of “any act of sedition”, Minister of State for Foreign Affairs Anwar Gargash said in a tweet.
Universities, schools and Aden’s only international airport had all been closed, witnesses said.
Dagher warned that separating south Yemen from the rest of the country would benefit the rebels and Iran, and said the situation in Aden was headed towards “total military confrontation”.
Sunday’s rally was called by the Southern Transitional Council, an autonomous body aimed at overseeing self-governance among southern provinces.
The 26-member council, which is not recognised by Hadi’s government, includes the governors of five southern provinces and two cabinet ministers.
Former Aden governor Aidarous al-Zoubeidi formed the council in May after Hadi fired him.
The council had asked Hadi to make changes in the government and gave him one week to do so — a deadline that expired on Sunday.
Armed supporters of the separatist Southern Movement patrol a street following clashes in the southern port city of Aden, Yemen, 28 January 2018 (AAP)AAP
Long campaign for secession
It had warned that if Hadi did not accept the demand, its supporters would begin a protest campaign to oust Dagher’s government.
The separatists have long campaigned for the secession of southern Yemen.
South Yemen was independent — with former British colony Aden as its capital — from its formation in 1967 until 1990, when it was unified with North Yemen under northern leader Ali Abdullah Saleh.
Four years later, it launched a separatist rebellion that culminated in its occupation by northern forces.
The Huthis, a northern Shiite minority, seized Sanaa in September 2014 with the help of Saleh and army units loyal to him.
In March 2015, the rebels advanced on Aden, where Hadi took refuge after escaping from Sanaa.
But the Saudi-led coalition helped pro-Hadi forces oust the rebels from Aden and four other provinces in July that year.
Hadi loyalists have been boosted by the Popular Resistance alliance of southern separatists and tribesmen after the rebels advanced on their regions.
Years of UN-backed peace efforts have failed to resolve Yemen’s conflict, which has killed more than 9,200 people and devastated a country already among the region’s poorest.
The Huthis have increasingly consolidated their grip on Sanaa and the north, especially since rebels killed Saleh in December after their alliance collapsed.